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Register a new userSystematic investigations of deep sub-barrier fusion reactions using an adiabatic approach
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Takatoshi Ichikawa
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To describe fusion hindrance observed in fusion reactions at extremely low incident energies, I propose a novel extension of the standard CC model by introducing a damping factor that describes a smooth transition from sudden to adiabatic processes. I demonstrate the performance of this model by systematically investigating various deep sub-barrier fusion reactions. I extend the standard CC model by introducing a damping factor into the coupling matrix elements in the standard CC model. I adopt the Yukawa-plus-exponential (YPE) model as a basic heavy ion-ion potential, which is advantageous for a unified description of the one- and two-body potentials. For the purpose of these systematic investigations, I approximate the one-body potential with a third-order polynomial function based on the YPE model. Calculated fusion cross sections for the medium-heavy mass systems of $^{64}$Ni + $^{64}$Ni, $^{58}$Ni + $^{58}$Ni, and $^{58}$Ni + $^{54}$Fe, the medium-light mass systems of $^{40}$Ca + $^{40}$Ca, $^{48}$Ca + $^{48}$Ca, and $^{24}$Mg + $^{30}$Si, and the mass-asymmetric systems of $^{48}$Ca + $^{96}$Zr and $^{16}$O + $^{208}$Pb are consistent with the experimental data. The astrophysical S factor and logarithmic derivative representations of these are also in good agreement with the experimental data. Since the results calculated with the damping factor are in excellent agreement with the experimental data in all systems, I conclude that the smooth transition from the sudden to adiabatic processes occurs and that a coordinate-dependent coupling strength is responsible for the fusion hindrance. In all systems, the potential energies at the touching point $V_{rm Touch}$ strongly correlate with the incident threshold energies for which the fusion hindrance starts to emerge, except for the medium-light mass systems.
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We demonstrate the damping of quantum octupole vibrations near the touching point when two colliding nuclei approach each other in the mass-asymmetric $^{208}$Pb + $^{16}$O system, for which the strong fusion hindrance was clearly observed. We, for the first time, apply the random-phase approximation method to the heavy-mass asymmetric di-nuclear system to calculate the transition strength $B$(E3) as a function of the center-of-mass distance. The obtained $B$(E3) strengths are substantially damped near the touching point, because the single-particle wave functions of the two nuclei strongly mix with each other and a neck is formed. The energy-weighted sums of $B$(E3) are also strongly correlated with the damping factor which is phenomenologically introduced in the standard coupled-channel calculations to reproduce the fusion hindrance. This strongly indicates that the damping of the quantum vibrations universally occurs in the deep sub-barrier fusion reactions.
Complete fusion excitation functions of reactions involving breakup are studied by using the empirical coupled-channel (ECC) model with breakup effects considered. An exponential function with two parameters is adopted to describe the prompt-breakup probability in the ECC model. These two parameters are fixed by fitting the measured prompt-breakup probability or the complete fusion cross sections. The suppression of complete fusion at energies above the Coulomb barrier is studied by comparing the data with the predictions from the ECC model without the breakup channel considered. The results show that the suppression of complete fusion are roughly independent of the target for the reactions involving the same projectile.
The tunneling of composite systems, where breakup may occur during the barrier penetration process is considered in connection with the fusion of halo-like radioactive, neutron- and proton-rich nuclei on heavy targets. The large amount of recent and new data clearly indicates that breakup hinders the fusion at near and below the Coulomb barrier energies. However, clear evidence for the halo enhancements, seems to over ride the breakup hindrance at lower energies, owing, to a large extent, to the extended matter density distribution. In particular we report here that at sub-barrier energies the fusion cross section of the Borromean two-neutron halo nucleus $^{6}$He with the actinide nucleus $^{238}$U is significantly enhanced compared to the fusion of a no-halo $^{6}$He. This conclusion differs from that of the original work, where it was claimed that no such enhancement ensues. This sub-barrier fusion enhancement was also observed in the $^{6}$He + $^{209}$% Bi system. The role of the corresponding easily excitable low lying dipole pygmy resonance in these systems is therefore significant. The consequence of this overall enhanced fusion of halo nuclei at sub-barrier energies, on stellar evolution and nucleosynthesis is evident.
The nuclear fusion is a reaction to form a compound nucleus. It plays an important role in several circumstances in nuclear physics as well as in nuclear astrophysics, such as synthesis of superheavy elements and nucleosynthesis in stars. Here we discuss two recent theoretical developments in heavy-ion fusion reactions at energies around the Coulomb barrier. The first topic is a generalization of the Wong formula for fusion cross sections in a single-channel problem. By introducing an energy dependence to the barrier parameters, we show that the generalized formula leads to results practically indistinguishable from a full quantal calculation, even for light symmetric systems such as $^{12}$C+$^{12}$C, for which fusion cross sections show an oscillatory behavior. We then discuss a semi-microscopic modeling of heavy-ion fusion reactions, which combine the coupled-channels approach to the state-of-the-art nuclear structure calculations for low-lying collective motions. We apply this method to subbarrier fusion reactions of $^{58}$Ni+$^{58}$Ni and $^{40}$Ca+$^{58}$Ni systems, and discuss the role of anharmonicity of the low-lying vibrational motions.
A large number of complete fusion excitation functions of reactions including the breakup channel were measured in recent decades, especially in the last few years. It allows us to investigate the systematic behavior of the breakup effects on the complete fusion cross sections. To this end, we perform a systematic study of the breakup effects on the complete fusion cross sections at energies above the Coulomb barrier. The reduced fusion functions F(x) are compared with the universal fusion functions which are used as a uniform standard reference. The complete fusion cross sections at energies above the Coulomb barrier are suppressed by the breakup of projectiles. This suppression effect for reactions induced by the same projectile is independent of the target and mainly determined by the lowest energy breakup channel of the projectile. There holds a good exponential relation between the suppression factor and the energy corresponding to the lowest breakup threshold.
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